Four-dimensional String Compactifications with D-Branes, Orientifolds and Fluxes

TL;DR

The article surveys four-dimensional string compactifications using D-branes, orientifolds, and fluxes, with a focus on constructing chiral vacua close to the supersymmetric Standard Model. It develops the technical toolkit: D-brane DBI/CS actions, orientifold projections, and Green-Schwarz anomaly cancellation, and then applies these to Type IIA/IIB setups with intersecting or magnetized branes, including toroidal, orbifold, and Gepner-model constructions. It also discusses moduli stabilization, gauge couplings, D-/F-terms, and the impact of fluxes on the 4D effective action, highlighting both the calculational framework and the phenomenological challenges. The review emphasizes both geometric and conformal-field-theory approaches, and demonstrates how consistency conditions like tadpole cancellation and K-theory constraints shape viable models, while also touching on statistical perspectives on vacua.

Abstract

This review article provides a pedagogical introduction into various classes of chiral string compactifications to four dimensions with D-branes and fluxes. The main concern is to provide all necessary technical tools to explicitly construct four-dimensional orientifold vacua, with the final aim to come as close as possible to the supersymmetric Standard Model. Furthermore, we outline the available methods to derive the resulting four-dimensional effective action. Finally, we summarize recent attempts to address the string vacuum problem via the statistical approach to D-brane models.

Figures (16)

• Figure 1: Closed string emitted from a D-brane: semi-infinite cylinder
• Figure 2: Open string: infinite strip with two boundaries
• Figure 3: Open string spectrum represented by quiver diagram
• Figure 4: One-loop partition function: tree-channel interpretation
• Figure 5: Two-dimensional torus $\mathbb T^2 = \mathbb C/{\Lambda}^2$ with two intersecting D-branes